Some math items that may be of interest:
- Zentralblatt Math has a review of Mochizuki’s IUT papers, by Peter Scholze. Scholze explains the problem with the proof claimed in these papers. For more details, see his manuscript with Stix, or this discussion hosted last year on this blog.
- The Bulletin of the AMS will be running a special issue on the work of Michael Atiyah. Available already are two wonderful articles: Michael Atiyah’s work in algebraic topology, by Graeme Segal, and The Atiyah-Singer index theorem, by Dan Freed.
- For a talk by Helmut Hofer about Andreas Floer and his work, together with contributions from others who knew Floer, see The Floer Jungle: 35 years of Floer theory.
- The latest AMS Notices has a memorial tribute to Steve Zucker, with a detailed discussion of his career and mathematical work. His collaborator David Cox explains that the origin of their collaboration was exactly what everyone has always suspected.
Update: The Scholze review has been removed (temporarily?). A cached version is here.
Update: The review was temporarily removed just because what was posted wasn’t a finalized version, this is explained here. They should repost once Scholze has a chance to make any final edits.
Update: The review is back up.
Update: Michael Harris has a new substack site, where he’ll be writing about the mechanization of mathematics. I’m glad to see someone doing this from his point of view.
Seems like Peter’s comments are removed/editted (?). Here’s the original (I think; found online):
Zentralblatt took down Scholze’s review and replaced it with the paper’s abstract. Here is a cached version of the review https://webcache.googleusercontent.com/search?q=cache:Lm7YcNafEeoJ:https://zbmath.org/pdf/07317908.pdf
That “review” of IUT 1 is a cut-and-paste of the abstract, as can be seen by comparing with the published version here: https://doi.org/10.4171/PRIMS/57-1-1
I haven’t compared with the published abstracts, but the other “reviews” of parts 2–4 look to be the same. If there was a review by Scholze, it’s been removed; I’d love to see it…
I see via Nalini Joshi on Twitter that the review was captured before it evaporated: https://web.archive.org/web/20210730194853/https://zbmath.org/pdf/07317908.pdf (and she alludes to the discussion on Reddit here: https://www.reddit.com/r/math/comments/ousg3s/scholzes_review_of_mochizukis_paper_for/)
If some kind of political pressure has been applied to remove this, then that is not a good look for anyone involved.
At the end of the Hofer’s nice history talk, Gromov – as is usual of him – makes some interesting general comments concerning Scholze’s condensed mathematics.
It seems to me that Helmut Hofers talk was at least partially meant to keep up discussing mathematical (work) culture and it’s possible effects.
That is – it is problematic to publicly discuss possible reasons for Andreas Floer’s -as the german Wikipedia writes unexpected– suicide, on the other hand it is not too far fetched to assume that his mathematical life took quite a role in his decisions. I therefore found it considerably well-balanced that Helmut Hofer mentioned in his talk in a matter-of-fact way some of the possible strains that may have impaired Andreas Floer.
So for example he mentioned that Andreas Floer may have had probably felt quite under pressure, when there was some kind of “hype” about his work and that people expected him to write up his results. He mentioned that Mathematics was not Andreas Floer sole passion, but that he played viola da gamba and thus that it was probably not easy to conciliate his other passions with his mathematical passions and (new) duties. Briefly after his death I had heard someone mentioning that Andreas Floer was quite probably suffering from something that could be somewhat called “stagefright” – another strain, which may come with job duties or at least with the roles a successful mathematician is often expected to fill in.
I had met him only very briefly before his death when he was a few days in Berlin. It may not be sensible to state the impressions I got from the very few interactions, as they are maybe simply too attached to particular moments – but in one instance he appeared to me quite deeply troubled. In the last interaction though he was sort of looking forward to his planned longer stay in Berlin and completed his farewell to me with something like a smiling “Bis dann” (see you soon). So I agree that his suicide didn’t appear to have been planned, but that it was -at least to me- rather -as Wikipedia writes- unexpected.
Nad, I wonder though if the “jungle” approach is just something made up by Hofer. Rare mathematicians do gain a wide knowledge of the waterfront early on. Yet may they still spend three months banging against a crack in the wall? I refer here to the story in the link of Floer taking three month to accomplish one of his goals after discussing it with a colleague. I admit some prejudice because Hofer seems so affable and interested in history, and he is looking for an answer to what happened.
(It does make me wonder though if I should have tried a more jungle approach when younger! I do remember reading somewhat widely, but without much effect.)
There’s also the issue of math anxiety, which can hit at any stage. Or, more likely in Floer’s case, locking up on a perfectionist writer’s block. I gather he enjoyed explaining his ideas in person.
I had problems to understand your comment.
do you mean “made up” versus “observed” or “made up” because it is an analogy or something else?
❓I rewatched the talk but I couldn’t find the story you are referring to:
Could you please say around which minute the story was told ?
❓A prejudice -in my understanding- is often something like an idea about “how objects happen/act in some time instance in past, present or future”. What do you mean by prejudice here:
Do you mean that you know what happened?